@SuperDicq Why indeed it can do that.

See `mpv --audio-device=help` and then select the right HDMI sound card.

i.e. `mpv --audio-device="alsa/hdmi:CARD=NVidia,DEV=0" <video>`

Your .asoundrc should then by default select only the headphone jack (which may not even need setting if the headphone jack is the default selected sound card, like on most computers);
defaults.pcm.!card x
defaults.pcm.!device y

As a result, the sound of the video player will only play over HDMI and the web browser will play only to the headphones.